Question: Simplify the following expression: $ q = \dfrac{-5}{6} + \dfrac{-y + 4}{9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-5}{6} \times \dfrac{9}{9} = \dfrac{-45}{54} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{-y + 4}{9} \times \dfrac{6}{6} = \dfrac{-6y + 24}{54} $ Therefore $ q = \dfrac{-45}{54} + \dfrac{-6y + 24}{54} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-45 - 6y + 24}{54} $ $q = \dfrac{-6y - 21}{54}$ Simplify the expression by dividing the numerator and denominator by 3: $q = \dfrac{-2y - 7}{18}$